Mark M$.$ Upp has just been fired as the university bookstore manager for setting prices too low $($only $20$ percent above suggested retail$).$ He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation.$$ There are two possible sites under consideration.$$ One is relatively small, while the other is large.$$ If he opens at Site $1$ and demand is high, he will generate a profit of $$50,000.$ If demand is low, he will lose $$10,000.$ If he opens at Site $2$ and demand is high, he will generate a profit of $$80,000,$ but he will lose $$30,000$ if demand is low.$$ He also has the option of not opening either.$$ He believes that there is a $50$ percent chance that demand will be high.$$ Mark can purchase a market research study. The probability of a good demand given a favorable study is $0\mathrm{.}8.$ The probability of a good demand given an unfavorable study is $0\mathrm{.}1.$ There is a $60$ percent chance that the study will be favorable.

The above problem context is for this question and the next a few questions in the same title.$$

What is Mark's maximum EMV with the market research study?